Wow! I kind of agree with the others. That is a lot of cooped up, not-much-scenery time for little else other than riding the trains.

I get it that you are a train fan and want to ride all the shinkansen routes. I just think I'd go about it a bit differently. First, I'd get rid of all those double-backs to spend the night in Tokyo. All shinkansen stops have nearby business traveler hotels that are cheap, convenient and often offer breakfast buffet with the room rate. Some have coin laundry facilities and wi-fi. If you are interested, I can recommend some decent places I have used at a few of your stops.

I wouldn't use those JR Pass days for sightseeing in Tokyo. Use the subway, it is cheaper, simpler and gets you everywhere. There are combo deals that include the train into the city from NRT and 2 days subway passes. Use the JR Pass for long distance travel.

If I were doing this (I wouldn't have the energy but if I were,) I'd buy the Keisei Skyliner+Metro Pass upon arrival at NRT, ride into the city on the Skyliner (one of my favorite trains) and stay near Ueno Station in Tokyo. Sight-see via subway from Ueno.

Then:

Rail Pass day 1: shinkansen Ueno-Sendai / visit Sendai a couple of hours / shinkansen Sendai-ShinAomori - double back to Akita - overnight Akita.

Day 2: local JR line Akita-Shinjo (scenic) / shinkansen Shinjo-Fukushima-Omiya-Niigata - overnight Niigata.

Day 3: shinkansen Niigata-Takasaki-Nagano / local JR line Nagano-Toyama-Takayama (via Hida Wideview) - overnight Takayama (see Takayama in pm)

Day 4: JR Ltd Exp Hida WV Takayama-Nagoya / shinkansen Nagoya-Okayama / Ltd Exp Nanpu Okayama-Kochi - overnight Kochi (Shikoku Island)

Day 5: Ltd Exp Nanpu Kochi-Okayama / shinkansen Okayama-Kagoshima-chuo - overnight Kagoshima.

Day 6: shinkansen Kagoshima-Hiroshima or Kyoto - overnight (pm sight-see)

Day 7: shinkansen back to Tokyo, perhaps stopping at Hakone for a few hours along the way. (I wouldn't, it's kind of a waste.)

It is entirely possible to schedule so Day 7 of the Pass is your departure day from Japan and just go Kyoto-Tokyo-NRT all at once, using the Pass to cover the Narita Express to the airport.

This is just an outline and some other sites/locations might be more appealing but it covers all the shinkansen lines you were interested in and still allows SOME visit time at and through some scenic locations. The limited express trains to/from Takayama and Kochi are beautiful rides.

Any way you look at it, this is a lot of time on trains.